Friday fun in Network Theory

For the first time, sociologists have mapped the romantic and sexual relationships of an entire high school over 18 months, providing evidence that these adolescent networks may be structured differently than researchers previously thought.

The results showed that, unlike many adult networks, there was no core group of very sexually active people at the high school. There were not many students who had many partners and who provided links to the rest of the community.

Instead, the romantic and sexual network at the school created long chains of connections that spread out through the community, with few places where students directly shared the same partners with each other. But they were indirectly linked, partner to partner to partner. One component of the network linked 288 students — more than half of those who were romantically active at the school — in one long chain.

Out of about 1,000 students in the school, the researchers interviewed 832 and found that slightly more than half reported having had sexual intercourse. They found 63 “simple pairs”, i.e., students whose only pairings were with each other. 189 students (35% of the romantically active population) belonged to networks containing three or fewer nodes. And then, if you want some really interesting topology,

The most striking feature of the network was a single component that connected 52 percent (288) of the romantically involved students at Jefferson. This means student A had relations with student B, who had relations with student C and so on, connecting all 288 of these students.

While this component is large, it has numerous short branches and is very broad â€“ the two most distant individuals are 37 steps apart. (Or to use a currently popular term, there were 37 degrees of separation between the two most-distant students.)

â€œFrom a studentâ€™s perspective, a large chain like this would boggle the mind,â€ [Ohio State professor James] Moody said. â€œThey might know that their partner had a previous partner. But they donâ€™t think about the fact that this partner had a previous partner, who had a partner, and so on.

â€œWhat this shows, for the first time, is that there are many of these links in a chain, going far beyond what anyone could see and hold in their head.â€

This caught my eye because I’ve actually dabbled in networks, studying protein structures using “motifs” — small sub-graphs with particular connection patterns whose preponderances we examine statistically. I’d be interested in getting the actual connection data, running them through MFinder and checking out their superfamily values.